The points will satisfy the standard equation of the linear system. Then the equation will be [tex]\rm y = 3x -5[/tex].
What is the linear system?
It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Given
x 2 3 4 5
y 1 4 7 10
let the linear equation y = mx + c.
For (2, 1), the equation will be
[tex]\rm 2m + c = 1[/tex] ...eq.1
For (3, 4), the equation will be
[tex]\rm 3m + c = 4[/tex] ...eq.2
Subtract equations 2 from 1, we have
[tex]\rm 3m + c -2m - c = 4 - 1[/tex]
On simplifying
[tex]\rm m = 3[/tex]
Substitute the value of m in equation 1, then we get
[tex]\rm 2*3+ c = 1[/tex]
On simplifying
[tex]\rm c = -5[/tex]
Thus, the equation will be [tex]\rm y = 3x -5[/tex].
More about the linear system link is given below.
https://brainly.com/question/20379472